There are two types of reports, fraudulent ones and real ones. The fraudulent ones will come from everywhere, while the real reports come only from pirate infested harbors. Therefore just subtract the mean report density and what remains should be random fluctuations around zero plus the real reports. So if a harbor has more than some threshold of reports, then it is pirate invested.
At this point in the discussion, you could probably correlate it with the number of the letters "R" in the reports. Because we all know that it's the pirates' favorite letter.
